Catheters are used to perform a variety of tasks within human bodies and other bodies including the delivery of medicine and fluids, the removal of bodily fluids, and the transport of surgical tools and instruments. In the diagnosis and treatment of atrial fibrillation, for example, catheters may be used to deliver electrodes to the heart for electrophysiological mapping of the surface of the heart and to deliver ablative energy to the surface, among other tasks. In order to properly administer treatment, the position and orientation of a catheter inside the body must be continuously monitored. One known technique for determining the position and orientation of a catheter within a body is by tracking a plurality of sensors on the catheter using a position sensing and navigation system (sometimes called a location mapping system). In one exemplary system offered for sale by St. Jude Medical, Inc., under the trademark “ENSITE NAVX”, the sensors comprise electrodes. Excitation of pairs of electrodes on the outer surface of the body generates electrical fields within the body. Voltage measurements on the catheter electrodes can then be used to determine the position and orientation of the catheter electrodes within a coordinate system of the position sensing and navigation system. Other exemplary position sensing and navigation systems include magnetic systems.
In order to provide information to clinicians about the position and orientation of the catheter, the determined position and orientation of the catheter sensors is often used to render an image of the catheter relative to surrounding tissues, including heart tissues. One drawback to conventional systems, however, is that the determined position and orientation of the catheter sensors is subject to systematic errors due to subtle differences in, e.g., sensor impedances and amplifier channels. These errors can distort the rendered shape of the catheter from its true mechanical shape in the resulting image.
Moreover, certain smoothing algorithms may not be suitable for circular or otherwise curved catheters. For example, smoothing algorithms that apply basis functions to model measured electrode positions as deviations from a straight line may not appropriately model catheters having substantial curvature. Implementing such smoothing algorithms on catheters having substantial curvature may induce errors such as a reduction in a diameter in the imaged catheter.